GATE CS 2002 Q1.14 — Number Representations (Fixed and Floating Point)

To convert the decimal fraction $0.25$ to its binary equivalent, we can express it as a sum of powers of $2$:

$$0.25 = \frac{1}{4} = \frac{1}{2^2} = 2^{-2}$$

In the binary positional number system, the positions to the right of the radix point represent negative powers of $2$:

$$(0.b_1 b_2 b_3 \dots)_2 = b_1 \times 2^{-1} + b_2 \times 2^{-2} + b_3 \times 2^{-3} + \dots$$

Comparing this with our value $2^{-2}$:

• $b_1 = 0$ (since there is no $2^{-1}$ term)
• $b_2 = 1$ (since we have $1 \times 2^{-2}$)
• $b_3 = b_4 = \dots = 0$

Thus, the binary representation of $0.25$ is $(0.01)_2$.

Therefore, the correct option is B.